A054014 Chowla function of n read modulo (the number of divisors of n).

0, 0, 0, 2, 0, 1, 0, 2, 0, 3, 0, 3, 0, 1, 0, 4, 0, 2, 0, 3, 2, 1, 0, 3, 2, 3, 0, 3, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 0, 1, 0, 5, 0, 3, 2, 1, 0, 5, 1, 0, 0, 3, 0, 1, 0, 7, 2, 3, 0, 11, 0, 1, 4, 6, 2, 5, 0, 3, 2, 1, 0, 2, 0, 3, 0, 3, 2, 1, 0, 5, 4, 3, 0, 7, 2, 1, 0, 3, 0, 11, 0, 3, 2, 1, 0, 11, 0, 0, 2, 8, 0, 1, 0

Offset: 1

Author

Asher Auel, Jan 17 2000

Keywords

• nonn

Comments

Chowla's function (A048050) = sum of divisors of n except 1 and n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005, A048050, A054013, A054015.

Programs

Maple

with(numtheory): [seq((sigma(i)-i-1) mod tau(i),i=1..120)];

Mathematica

Array[Mod[DivisorSigma[1, #] - # - 1, DivisorSigma[0, #]] &, 103] (* Michael De Vlieger, Oct 30 2017 *)

PARI

A054014(n) = ((sigma(n)-n-1) % numdiv(n)); \\ Antti Karttunen, Oct 30 2017

Formula

a(n) = A048050(n) mod A000005(n).